Important Remark

1. To find the coordinates of the point of intersection of two non – parallel lines, we solve the given equations simultaneously and the values of x and y so obtained determine the coordinates of the point of intersection.

Condition of Concurrency of three lines

Three lines are said to be concurrent if they pass through a common point i.e. they meet at a point.Thus, if three lines are concurrent the point of intersection of two lines lies on the third line. Leta1x + b1y + c1 = 0 – (i)a2x + b2y + c2 = 0 – (ii)a3x + b3y + c3 = 0 – (iii)be three concurrent lines.Then the point of intersection of (i) and (ii) must lie on the third. The coordinates of the point of intersection of (i) and (ii) are b1c2 – b¬2c1, c1a2 – c2a1 a1b2 – a2b1 a1b2 – a2b1This point must lie on (iii)Therefore, a3 b1c2 – b¬2c1 + b3 c1a2 – c2a1 + c3 = 0 a1b2 – a2b1 a1b2 – a2b1a3(b1c2 – b2c1) + b3(c1a2 – c2a1) + c3(a1b2 – a2b1) = 0

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